"Using mostly my voice, I solved one of @EpochAIResearch 's FrontierMath Open Problems: finding an explicit presentation of the 2-adic Absolute Galois Group - open for more than forty years, now with a full proof in collaboration with David Roe, the problem's proposer. 1/n"
This problem is the second in the set of FrontierMath Open Problems to 'fall,' and the first under the 'Solid result' tier. Is this going to be a 'slowly, then all at once' moment? These days it's hard to tell. 2/n The problem sat open while other parts of group theory around it unraveled in the 80s: Jannsen & Wingberg wrote down generators and relations for the absolute 3-adic, 5-adic etc Galois Groups, for odd primes, in 1982. The prime 2 never followed, through decades of attempts. 3/n The problem-solving infrastructure was already in place from my Erdős-problem-solving runs: I drove Claude Code as the operational controller using (newly) my voice, to operate ChatGPT research harnesses; plus speech-to-text to instruct ChatGPT to push on the manuscript. 4/n GPT-5.6 Pro was in stealth deployment in mid-June (the browser still said 5.5, but it was obvious). In a ~26-hour autonomous stretch it found a candidate, "A2," and built a proof and a manuscript around it. A2 passed the finite-group tests my local computational package ran. 5/n A2 was still wrong, despite having a long proof to back it up: a fresh review by GPT-5.6 caught a lone wrong, unrepairable lemma in its 60-page proof manuscript. When asked to modify the candidate to make the proof 'fit', GPT-5.6 came up with the solution we have today. 6/n — David Turturean
Source: https://x.com/DavidTurturean/status/2081780318881677693